If the speed of a particle triples, by what factor does its kinetic energy increase?

An alternate sol is that K. E is directly proportional to the square of the speed, so the increase of speed by three times means the K. E becomes square of the speed, i. e, it becomes 3^2=9 times. If the Speed is increased by 3, then the Kinetic energy increases by 9.

Kinetic energy = (1/2) (mass) (speed) ².

See that little ² there on the end? That tells us that kinetic energy is proportional to the square of the speed.

If the speed of the moving object triples, then the moving object has 3² or nine times as much kinetic energy as it had before.

A better way to look at it is: If you want to triple the speed of a moving object, it's not enough to just give it 3 times as much kinetic energy as it has now. You have to give it 9 times as much as it has now.